Jesus answered this question on several occasions:
Luke 13:14-16 - But the synagogue leader was indignant that Jesus had
healed on the Sabbath. “There are six days for work,” he told the
crowd. “So come and be healed on those days and not on the Sabbath.”
“You hypocrites!” the Lord replied. “Does not each of you on the
Sabbath untie his ox or donkey from the stall and lead it to water?
Then should not this daughter of Abraham, whom Satan has kept bound
for eighteen long years, be released from her bondage on the Sabbath
Matt 12:2-5 - When the Pharisees saw this, they said to Him, “Look,
Your disciples are doing what is unlawful on the Sabbath.”
Jesus replied, “Have you not read what David did when he and his
companions were hungry? He entered the house of God, and he and his
companions ate the consecrated bread, which was not lawful for them
to eat, but only for the priests.
Or haven’t you read in the Law that on the Sabbath the priests in the
temple break the Sabbath and yet are innocent? But I tell you that
something greater than the temple is here.
Mark 3:2-5 - In order to accuse Jesus, they were watching to see if He
would heal on the Sabbath.
Then Jesus said to the man with the withered hand, “Stand up among
us.” 4And He asked them, “Which is lawful on the Sabbath: to do good
or to do evil, to save life or to destroy it?”
But they were silent. Jesus looked around at them with anger and
sorrow at their hardness of heart. Then He said to the man, “Stretch
out your hand.” So he stretched it out, and it was restored.
Luke 14:2-5 - Right there before Him was a man with dropsy. So Jesus
asked the experts in the law and the Pharisees, “Is it lawful to heal
on the Sabbath or not?”
But they remained silent. Then Jesus took hold of the man, healed him,
and sent him on his way. And He asked them, “Which of you whose son or
ox falls into a pit on the Sabbath day will not immediately pull him
John 5:7-9 - “Sir,” the invalid replied, “I have no one to help me
into the pool when the water is stirred. While I am on my way, someone
else goes in before me.”
Then Jesus told him, “Get up, pick up your mat, and walk.” Immediately
the man was made well, and he picked up his mat and began to walk.
Now this happened on the Sabbath day
Thus, Jesus' approach to Sabbath-keeping and its associated "holiness" or better, "separateness" was to sanctify in a practical way without making it a burden as illustrated by the above examples.
The Sabbath was intended to be a festival of celebration "to the LORD" (Ex 20:10, Isa 58:13) and a "delight" (Isa 58:14) because it was "the LORD's Day, and honorable" (Isa 58:14, Matt 12:8, Mark 2:28, Luke 6:5).
The same practical attitude appears in the incident of both Num 15:34 and the conquest of Jericho (Josh 6: 3, 14, 15), and in that recorded in 1 Sam 21:1-6 concerning David and the shew bread.
Israel at this time did not have a salaried army nor police force. Therefore, the guarding was presumably done by some volunteers who were otherwise occupied with other things - they were not paid for this service to guard.